Hybrid Quantum Classical Calculations

This document details the implementation of hybrid quantum-classical calculations, combining classical DFT with quantum computing methods through active space embedding.

Implementation Overview

Classical Component (CP2K)

  • PBE exchange-correlation functional with GGA

  • GPW method (500 Ry plane-wave cutoff, 60 Ry relative cutoff)

  • DZVP-MOLOPT-GTH basis sets

  • DFT-D3 dispersion correction

  • Periodic boundary conditions with 25 Å vacuum gap

  • 4×4 supercell of Al(111)

  • Fermi-Dirac distribution (1000 K electronic temperature)

Quantum Component (Qiskit)

  • Active space: 2 electrons in 5 orbitals

  • ADAPT-VQE algorithm implementation

  • UCCSD ansatz

  • SPSA optimizer configuration:

    optimizer = SPSA(
    maxiter=1000,
    learning_rate=0.005,
    perturbation=0.05,
    last_avg=1
)

Workflow Structure

  1. Classical DFT Calculation (CP2K)

    # Run CP2K calculation with active space embedding
cp2k -i Al111_active_space.inp

  2. Quantum Computation (ADAPT-VQE)

    # Execute quantum calculation with specified parameters
python client-vqe-ucc.py --nalpha 1 --nbeta 1 --norbs 5 --adapt

  3. Integration and Execution

    # Combined workflow execution
./run.sh

Active Space Configuration

The active space calculation is configured in CP2K with the following key parameters:

&ACTIVE_SPACE
  ACTIVE_ELECTRONS 2        # Number of active electrons
  ACTIVE_ORBITALS 5        # Number of active orbitals
  SCF_EMBEDDING TRUE       # Enable SCF embedding
  EPS_ITER 1E-6           # Convergence criterion for embedding iterations
  MAX_ITER 100            # Maximum number of embedding iterations
  AS_SOLVER QISKIT        # Using Qiskit as the active space solver
  ORBITAL_SELECTION CANONICAL  # Method for selecting active orbitals

Key Components

  • Active Space Size: 2 electrons in 5 orbitals around the Fermi level

  • Embedding Method: Self-consistent field (SCF) embedding with convergence threshold of 1E-6

  • Orbital Selection: Using canonical orbitals (energy-ordered) for active space selection

ERI Configuration

&ERI
  METHOD FULL_GPW        # Full Gaussian and Plane Waves method
  PERIODICITY 1 1 1      # Periodic boundary conditions in all directions
  OPERATOR <1/r>         # Coulomb operator for electron repulsion
&END ERI

&ERI_GPW
  CUTOFF 500            # Plane wave cutoff for ERI calculation
  REL_CUTOFF 60         # Relative cutoff for GPW method
&END ERI_GPW

The active space solver (Qiskit) receives the one- and two-electron integrals through FCIDUMP format, enabling seamless integration between the classical DFT calculation in CP2K and the quantum computation of the active space using VQE.

Key Features

  • Socket-based communication between CP2K and Qiskit

  • Active space transformation for periodic systems

  • Multiple VQE implementations:

    • Standard VQE with UCCSD

    • AdaptVQE with dynamic ansatz

    • StatefulVQE with warm-starting

    • StatefulAdaptVQE

Implementation Files

The complete implementation details can be found in the following documentation:

Source files: